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The question is in the photo

The question is in the photo-example-1
User Aaliyah
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1 Answer

6 votes

Answer:

A=1, B=-1, C=-7, D=15

Explanation:

Off the top of my head, i can't remember the name of the rule, but if a function has a root of (a+bi), then it must also have a root of (a-bi).

You have a cubic polynomial, so it must have 3 roots. 2 roots are already given to you. Using the rule above, you can find the 3rd root, which would be (2-i).

So we have -3, (2+i), and (2-i). You can construct the equation by adding x to the additive inverse of each, giving you (x-(-3)), (x-(2+i)), and (x-(2-i))

Simplify then multiply all roots together to get the expanded polynomial. the coefficients are your answer.

(x+3)(x-(2-i))(x-(2+i))

(x-3)(x^2-4x+5)

x^3-x^2-7x+15

User BUY
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